Growth and surface morphology of epitaxial Fe(110)/MgO(111)/Fe(110) trilayers constituting a magnetic tunnel junction were investigated by low-energy electron diffraction (LEED) and scanning tunneling microscopy (STM). STM reveals a grain-like growth mode of MgO on Fe(110) resulting in dense MgO(111) films at room temperature as well as at 250°C. As observed by STM, initial deposition of MgO leads to a partial oxidation of the Fe(110) surface which is confirmed by Auger electron spectroscopy. The top Fe layer deposited on Mg(111) at room temperature is relatively rough consisting of clusters which can be transformed by annealing to an atomically flat epitaxial Fe(110) film.